Question: What do the following two equations represent? $4x+3y = 5$ $-12x+16y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $4x+3y = 5$ $3y = -4x+5$ $y = -\dfrac{4}{3}x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $-12x+16y = 5$ $16y = 12x+5$ $y = \dfrac{3}{4}x + \dfrac{5}{16}$ The slopes are negative inverses of each other, so the lines are perpendicular.